Question

use the half-angle formula to evaluate tan(17pi/12)

Answer 1

\(\bf \cfrac{17}{12}\cdot 2\implies \cfrac{17}{6}\implies \cfrac{12+5}{6}\implies \cfrac{12}{6}+\cfrac{5}{6}\implies 2+\cfrac{5}{6}\qquad thus
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\cfrac{17\pi }{12}\cdot 2\implies \cfrac{17\pi }{6}\implies \cfrac{12\pi +5\pi }{6}\implies \cfrac{12\pi }{6}+\cfrac{5\pi }{6}\implies 2\pi +\cfrac{5\pi }{6}\qquad thus
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\cfrac{\frac{17\pi }{12}\cdot 2}{2}\implies \cfrac{17\pi }{12}\qquad thus\qquad \cfrac{2\pi +\frac{5\pi }{6}}{2}\implies \cfrac{17\pi }{12}\)

Answer 2

anyhow... to use the half-angle identity
simply multiply the angle given, by 2
and use that in the half-angle identity

Answer 3

\(\bf 2\pi +\cfrac{5\pi }{6}\) means one "go around" and then it lands on \(\bf \cfrac{5\pi }{6}\)

so \(\bf 2\pi +\cfrac{5\pi }{6}\) is coterminal with \(\bf \cfrac{5\pi }{6}\)

Answer 4

so 2pi+(5pi/6)/2 ----17pi/12 is the answer